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Practice the questions given in the worksheet on Remainder Theorem.
1. Use the Remainder Theorem, find the remainder when 4x3 - 3x2 + 2x - 4 is divided by x + 1.
2. If p(y) = y3 + y2 - 2y + 1, using Remainder Theorem, find the remainder, when p(y) is divided by (y – 3), find the value of p(a).
3. Find the remainder (without division) when
(a) x2 - 2x + 4 is divided by x - 1
(b) 2x3 - 3x2 + 7x - 8 is divided by x - 1
4. Use the Remainder Theorem, find the remainder when x4 - 3x2 + 4x - 12 is divided by x - 3.
5. Find the remainder (without division) when
(a) x3 + 4x + 2 is divisible by x + 2
(b) 4x3 - 3x2 + 5x + 4 is divided by 2x + 1
(c) 4x3 + 5x2 + 6x - 7 is divided by 2x - 1
6. What number should be added to x2 + 5 so that the resulting polynomial leaves the remainder 3 when divided by x + 3?
7. Use the Remainder Theorem, find the remainder when 4x3 - 3x2 + 2x - 4 is divided by x + 1.
8. What number should be subtracted from 3x2 + 5x so that the resulting polynomial leaves the remainder 1 when divided by 2x + 5?
9. Use the Remainder Theorem, find the remainder when x6 + 3x2 + 10 is divided by x - 2.
10. Find a if the remainder is a when x3 + 3x2 - ax + 3 is divided by x - 2.
11. If the polynomials ax3 + 4x2 + 3x – 4 and x3 - 4x + a leave the same remainder when divided by (x - 3), find the value of a.
12. Find the value of k if the remainder is -3 when kx3 + 8x2 - 4x + 10 is divided by x +1.
13. If both ax3 + 2x2 - 3 and x2 - ax + 4 leave the same remainder when divided by x - 2, find a.
Answers for the worksheet on Remainder Theorem are given below:
Answers:
1. -13
2. 31, a3 + a2 - 2a + 1
3. (a) 3
(b) -2
4. 54
5. (a) -14
(b) 14
(c) -94
6. -11
7. -13
8. 214
9. 86
10. 233
11. a = -1.
12. 25
13. 310
● Factorization
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